A FIFA judge has cleared Russia and Qatar of corruption in their winning bids for the next two World Cups.

German judge Joachim Eckert formally closed FIFA's probe into the 2018 and 2022 World Cup bidding contests on Thursday, almost four years after the vote by the governing body's scandal-tainted executive committee.

Eckert noted wrongdoing among the 11 bidding nations in a 42-page summary of FIFA prosecutor Michael Garcia's investigations.

However, Eckert ruled that the integrity of the December 2010 voting results was not affected.

No proof was found of longstanding allegations of bribes and voting pacts. Eckert concluded that any rule-breaking behavior was "far from reaching any threshold" to require re-running the contests.

Eckert wants Garcia to prosecute cases against individual FIFA voters and bid staffers.